Application of Genetic Algorithm in Multi-objective Optimization

David Schaffer [33] proposed the first multi-objective GA in 1980, named Vector evaluated GA
(VEGA), with a limitation of having the search direction parallel to the axes of the objective space.
Two approaches were suggested to improve VEGA. Following the work of Schaffer, a good
number of multi-objective GAs has been developed and suggested by various researchers with
variation in framework and operator [1, 19]. A complete list of these popular multi-objective GA
approaches with their advantages and disadvantages have been discussed by Konak et.al [32]. Some
of them are mentioned here [33-44]: Vector Evaluated GA (VEGA), Vector Optimized Evolution
Strategy (VOES), Weight-Based GA (WBGA), Multiple Objective GA (MOGA), Niched Pareto GA
(NPGA, NPGA2), Non-dominated Sorting GA (NSGA,NSGA-II), Distance-Based Pareto GA
(DPGA),Thermo-dynamical GA (TDGA), Strength Pareto Evolutionary Algorithm (SPEA,
SPEA2), Multi-Objective Messy GA (MOMGA-I, II, III), Pareto Archived Evolution Strategy
(PAES), Pareto Enveloped Based Selection Algorithm (PESA, PESA-II), and Micro GA-MOEA
(GA, GA2).
Among all these methods, determining which one is the best-performed technique has become a
very common question in the research field of multi-objective optimization. Several test problems
have been designed and developed by scientists and researchers and these techniques have been
applied to solve them. However, the most representative, discussed and compared evolutionary
algorithms are Strength Pareto Evolutionary Algorithm (SPEA, SPEA2), Pareto Archived Evolution
Strategy (PAES), Pareto Enveloped Based Selection Algorithm (PESA, PESA-II), and a Nondominated
Sorting GA (NSGA-II). Several comparison studies and numerical simulations using
various test cases exhibit NSGA-II and SPEA2 as better MOEA technique than other methods.
Even for multi-objective optimization having more than two objectives, SPEA2 seems more
advantageous over NSGA-II.
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